Dr Tewari has developed computational resources with an expansible object-oriented framework in Java for handling exact coalescent recursions and doing Monte Carlo simulations with importance sampling. We have advanced our combinatorial understanding of coalescent results, resulting in concrete improvements to coalescent algorithms. In particular, Drs. Tewari and Spouge have discovered a general means of accelerating coalescent recursions and have implemented it within the Java framework, to evaluate its practical implications.